Interface Constraints on Shear Band Patterns in Bonded Metallic Glass Films Under Microindentation

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behavior of bulk metallic glasses (BMGs) corresponds to strain localization into narrow shear bands, and these shear bands, if unconstrained, may catastrophically propagate throughout the specimen.[1–4] It has been widely demonstrated that if the shear bands can be blocked by external or internal constraints, the plastic strain on each shear band is minimized and therefore additional shear bands have to be initiated to accommodate the applied strain fields, thus delaying the catastrophic failure and leading to enhanced ductility.[5–9] Consequently, the understanding of shear band patterns will help design these constraints to confine shear bands and to prevent brittle failure of BMGs. Z.N. AN, W.D. LI, and F.X. LIU, Graduate Students, and P.K. LIAW, Professor, are with the Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN 37996. Y.F. GAO, Associate Professor, Department of Materials Science and Engineering, University of Tennessee, is also a Joint Faculty Member, with the Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831. Contact e-mail: [email protected] Manuscript submitted July 5, 2011. Article published online January 19, 2012 METALLURGICAL AND MATERIALS TRANSACTIONS A

It has been found that shear bands in BMGs deviate, although slightly, from the principal shear stress directions. In uniaxial tension and compression tests of BMGs, the angle between shear band plane and loading direction falls in the range of 50 to 60 deg for tension tests and 40 to 45 deg for compression test.[10–16] Such deviation was explained using the Mohr–Coulomb yield criterion.[10–15] As pointed out by Zhao and Li,[17,18] the Mohr–Coulomb model, however, gives the same amount of deviation in both tension and compression conditions, and therefore is unable to predict the observed asymmetric deviation of shear band angles from 45 deg in tension and compression tests. In our recent work,[19] shear bands in metallic glasses are modeled as a result of material instability (which can be predicted from constitutive parameters and loading conditions), which does not corresponds to material yield condition. Using the classic Rudnicki–Rice model,[20] we found that the shear band directions depend on Poisson’s ratio m, the ratios of three deviatoric principal stresses to Mises stress, the coefficient of internal friction l, and the dilatancy factor b. As shown in Figure 1, the shear band makes an angle h0 to the largest principal stress rI with VOLUME 43A, AUGUST 2012—2729

σI

σII

σIII

σIII 0

σII σI Fig. 1—Schematic illustration of the shear band direction in the principal stress space with principal stresses rI  rII  rIII .

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n  Nmin h0 ¼  tan1 Nmax  n

½1

 n ¼ 13 ð1 þ mÞðb þ lÞ  N ð1pffiffiffi mÞ; Nmax ¼ r0I s; N ¼ where  r0II s; Nmin ¼ r0III s; s ¼ rmises 3; and r0I , r0II , and r0III are the principal deviatoric stresses. On ðrI ; rII Þ and ðrII ; rIII Þ planes, there will be only one kind of shear band, which is parallel to the rII d

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